Transcript 4.1 Notes

4.1 – Right Triangle
Trigonometry
Objectives: You should be able to find values of trig
functions in right triangles and solve right triangles.
Example 1: Find the exact values of the
six trigonometric functions of θ.
Example 2: If
, find the exact values of
the five remaining trigonometric functions for the
acute angle .
Find a Missing Side Length
Example 3: Find the value of x. Round to
the nearest tenth, if necessary.
Example 4: SPORTS A competitor in a hiking
competition must climb up the inclined course
as shown to reach the finish line. Determine the
distance in feet that the competitor must hike to
reach the finish line.
Find a Missing Angle Measure
Example 5: Use a trigonometric function
to find the measure of θ. Round to the
nearest degree, if necessary.
Angle of Elevation & Angle of Depression
 What do we know about Angles of
Elevation and Depression???
Example 6: SKIING The chair lift at a ski
resort rises at an angle of 20.75° while
traveling up the side of a mountain and attains
a vertical height of 1200 feet when it reaches
the top. How far does the chair lift travel up the
side of the mountain?
Example 7: AIRPLANE A person on an
airplane looks down at a point on the ground at
an angle of depression of 15°. The plane is
flying at an altitude of 10,000 feet. How far is
the person from the point on the ground to the
nearest foot?
Example 8: SIGHTSEEING A sightseer on
vacation looks down into a deep canyon using
binoculars. The angles of depression to the far
bank and near bank of the river below are 61°
and 63°, respectively. If the canyon is 1250 feet
deep, how wide is the river?
Example 9: HIKING The angle of elevation
from a hiker to the top of a mountain is 25o.
After the hiker walks 1000 feet closer to the
mountain the angle of elevation is 28o. How
tall is the mountain?
A. 3791 ft
B. 4294 ft
C. 7130 ft
D. 8970 ft
Solve a Right Triangle
Example 10: Solve ΔFGH. Round side
lengths to the nearest tenth and angle
measures to the nearest degree.
Exact Values: Hand-Jive
Example 11: Find exact value without calc.
a. sin 45º
b. cos 30º
c. tan 60º
d. sec 60º
e. cot 30º
f. csc 45º
Example 13: >, <, or = ? Without calc.
a. sin 45º ____ cot 60º
b. tan 45º ____ sec 30º